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PROCEEDINGS OF JAPAN EARTHQUAKE ENGINEERING SYMPOSIUM
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Yutaka MATSUSHIMA
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SPECTRA OF SPATIALLY VARIANT GROUND MOTIONS AND ASSOCIATED TRANSFER FUNCTIONS OF SOIL-FOUNDATION SYSTEM
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The movement of ground surface during an earthquake would not be identical even in relatively limited plane, but possible to have spatial variation. In this sense mathematical expressions of cross spectral density functions among such ground motions have been investigated from various standpoints, from which associated transfer functions of soilfoundation system have been analytically derived herein. This paper mainly consists of the following contents. In Section 2 some earthquake observations performed in past both on the building foundation and on ground surface in its vicinity are reviewed from abovementioned point of view. Section 3 describes the technique by which the response of rigid foundation due to multiple inputs is evaluated in a frequency domain through the probabilistic theory. In Section 4 the cross spectral density functions of statistically correlated ground motions are expressed in mathematical forms together with corresponding transfer functions of soil-foundation system obtained by the method discussed in Section 3, the results of which are compared with those of observations shown in Section 2. Ground motions with phase difference in addition are also dealt with in Section 5. As the results, the spectral expression of ground motions which have the statistical correlation depending only on the distance and the associated transfer function will be recommended as the most simple and realistic simulation of the actual phenomenon, although available data are not enough both in quantity and in quality to state definitely. The single parameter in this case is a constant called "space correlation Index", the value of which has been estimated.
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